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Measuring the Autocorrelation Function of Nanoscale Three-Dimensional Density Distribution in Individual Cells Using Scanning Transmission Electron Microscopy, Atomic Force Microscopy, and a New Deconvolution Algorithm

  • Yue Li (a1), Di Zhang (a2), Ilker Capoglu (a2), Karl A. Hujsak (a3), Dhwanil Damania (a2), Lusik Cherkezyan (a2), Eric Roth (a3), Reiner Bleher (a3), Jinsong S. Wu (a3), Hariharan Subramanian (a2), Vinayak P. Dravid (a3) (a4) and Vadim Backman (a2) (a4)...

Essentially all biological processes are highly dependent on the nanoscale architecture of the cellular components where these processes take place. Statistical measures, such as the autocorrelation function (ACF) of the three-dimensional (3D) mass–density distribution, are widely used to characterize cellular nanostructure. However, conventional methods of reconstruction of the deterministic 3D mass–density distribution, from which these statistical measures can be calculated, have been inadequate for thick biological structures, such as whole cells, due to the conflict between the need for nanoscale resolution and its inverse relationship with thickness after conventional tomographic reconstruction. To tackle the problem, we have developed a robust method to calculate the ACF of the 3D mass–density distribution without tomography. Assuming the biological mass distribution is isotropic, our method allows for accurate statistical characterization of the 3D mass–density distribution by ACF with two data sets: a single projection image by scanning transmission electron microscopy and a thickness map by atomic force microscopy. Here we present validation of the ACF reconstruction algorithm, as well as its application to calculate the statistics of the 3D distribution of mass–density in a region containing the nucleus of an entire mammalian cell. This method may provide important insights into architectural changes that accompany cellular processes.

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Bancaud A., Huet S., Daigle N., Mozziconacci J., Beaudouin J. & Ellenberg J. (2009). Molecular crowding affects diffusion and binding of nuclear proteins in heterochromatin and reveals the fractal organization of chromatin. EMBO J 28(24), 37853798.
Bancaud A., Lavelle C., Huet S. & Ellenberg J. (2012). A fractal model for nuclear organization: Current evidence and biological implications. Nucleic Acids Res 40(18), 87838792.
Barer R. (1957). Refractometry and interferometry of living cells. J Opt Soc Am 47(6), 545556.
Barer R. & Tkaczyk S. (1954). Refractive index of concentrated protein solutions. Nature 173(4409), 821822.
Baumeister W., Grimm R. & Walz J. (1999). Electron tomography of molecules and cells. Trends Cell Biol 9(2), 8185.
Bedin V., Adam R.L., de Sá B.C., Landman G. & Metze K. (2010). Fractal dimension of chromatin is an independent prognostic factor for survival in melanoma. BMC Cancer 10(1), 260.
Biskupek J., Leschner J., Walther P. & Kaiser U. (2010). Optimization of STEM tomography acquisition—A comparison of convergent beam and parallel beam STEM tomography. Ultramicroscopy 110(9), 12311237.
Cherkezyan L., Capoglu I., Subramanian H., Rogers J., Damania D., Taflove A. & Backman V. (2013). Interferometric spectroscopy of scattered light can quantify the statistics of subdiffractional refractive-index fluctuations. Phys Rev Lett 111(3), 033903.
Cherkezyan L., Stypula-Cyrus Y., Subramanian H., White C., Cruz M.D., Wali R.K., Goldberg M.J., Bianchi L.K., Roy H.K. & Backman V. (2014). Nanoscale changes in chromatin organization represent the initial steps of tumorigenesis: A transmission electron microscopy study. BMC Cancer 14(1), 1.
Choudhuri K., Llodrá J., Roth E.W., Tsai J., Gordo S., Wucherpfennig K.W., Kam L., Stokes D.L. & Dustin M.L. (2014). Polarized release of TCR-enriched microvesicles at the T cell immunological synapse. Nature 507(7490), 118.
Damania D., Roy H.K., Subramanian H., Weinberg D.S., Rex D.K., Goldberg M.J., Muldoon J., Cherkezyan L., Zhu Y. & Bianchi L.K. (2012). Nanocytology of rectal colonocytes to assess risk of colon cancer based on field cancerization. Cancer Res 72(11), 27202727.
Davies H., Wilkins M., Chayen J. & La Cour L. (1954). The use of the interference microscope to determine dry mass in living cells and as a quantitative cytochemical method. J Cell Sci 3(31), 271304.
Metze K. (2013). Fractal dimension of chromatin: Potential molecular diagnostic applications for cancer prognosis. Expert Rev Mol Diagn 13(7), 719735.
Midgley P. & Weyland M. (2003). 3D electron microscopy in the physical sciences: The development of Z-contrast and EFTEM tomography. Ultramicroscopy 96(3), 413431.
Mirny L.A. (2011). The fractal globule as a model of chromatin architecture in the cell. Chromosome Res 19(1), 3751.
Radosevich A.J., Mutyal N.N., Eshein A., Gould B., Rogers J.D., Goldberg M.J., Bianchi L.K., Yen E.F., Konda V. & Rex D.K. (2015). Rectal optical markers for in vivo risk stratification of premalignant colorectal lesions. Clin Cancer Res 21(19), 43474355.
Rogers J.D., Radosevich A.J., Yi J. & Backman V. (2014). Modeling light scattering in tissue as continuous random media using a versatile refractive index correlation function. IEEE J Sel Top Quantum Electron 20(2), 173186.
Schmitt J.M. & Kumar G. (1998). Optical scattering properties of soft tissue: A discrete particle model. Appl Opt 37(13), 27882797.
Sousa A.A. & Leapman R.D. (2012). Development and application of STEM for the biological sciences. Ultramicroscopy 123, 3849.
Subramanian H., Roy H.K., Pradhan P., Goldberg M.J., Muldoon J., Brand R.E., Sturgis C., Hensing T., Ray D. & Bogojevic A. (2009). Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy. Cancer Res 69(13), 53575363.
Yakushevska A., Lebbink M., Geerts W., Spek L., Van Donselaar E., Jansen K., Humbel B., Post J., Verkleij A. & Koster A. (2007). STEM tomography in cell biology. J Struct Biol 159(3), 381391.
Yi J., Radosevich A.J., Stypula-Cyrus Y., Mutyal N.N., Azarin S.M., Horcher E., Goldberg M.J., Bianchi L.K., Bajaj S. & Roy H.K. (2014). Spatially resolved optical and ultrastructural properties of colorectal and pancreatic field carcinogenesis observed by inverse spectroscopic optical coherence tomography. J Biomed Opt 19(3), 036013036013.
Zhang D., Capoglu I., Li Y., Cherkezyan L., Chandler J., Spicer G., Subramanian H., Taflove A. & Backman V. (2016). Finite-difference time-domain-based optical microscopy simulation of dispersive media facilitates the development of optical imaging techniques. J Biomed Opt 21(6), 065004065004.
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Microscopy and Microanalysis
  • ISSN: 1431-9276
  • EISSN: 1435-8115
  • URL: /core/journals/microscopy-and-microanalysis
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